Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / communications-1.1.1 / egolaydec.m

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+## Copyright (C) 2007 Muthiah Annamalai <muthiah.annamalai@uta.edu>
+##
+## This program is free software; you can redistribute it and/or modify it under
+## the terms of the GNU General Public License as published by the Free Software
+## Foundation; either version 3 of the License, or (at your option) any later
+## version.
+##
+## This program is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {}  egolaydec (@var{R})
+## 
+## Given @var{R}, the received Extended Golay code, this function tries to
+## decode @var{R} using the Extended Golay code parity check matrix.
+## Extended Golay code (24,12) which can correct upto 3 errors.
+##
+## The received code @var{R}, needs to be of length Nx24, for encoding. We can
+## decode several codes at once, if they are stacked as a matrix of 24columns,
+## each code in a separate row.
+##
+## The generator G used in here is same as obtained from the
+## function egolaygen. 
+##
+## The function returns the error-corrected code word from the received
+## word. If decoding failed, the second return value is 1, otherwise it is 0.
+## 
+## Extended Golay code (24,12) which can correct upto 3
+## errors. Decoding algorithm follows from Lin & Costello.
+## 
+## Ref: Lin & Costello, pg 128, Ch4, 'Error Control Coding', 2nd ed, Pearson.
+##
+## @example
+## @group
+##  M=[rand(10,12)>0.5]; 
+##  C1=egolayenc(M); 
+##  C1(:,1)=mod(C1(:,1)+1,2)
+##  C2=egolaydec(C1)
+## @end group
+## @end example
+##
+## @end deftypefn
+## @seealso{egolaygen,egolayenc}
+
+function [C,dec_error]=egolaydec(R)
+
+  if ( nargin < 1 )
+    error('usage: C=egolaydec(R)');
+  elseif ( columns(R) ~= 24 )
+    error('extended golay code is (24,12), use rx codeword of 24 bit column size');
+  end
+
+  I=eye(12);
+                                %P is 12x12 matrix
+  P=[1 0 0 0 1 1 1 0 1 1 0 1;
+     0 0 0 1 1 1 0 1 1 0 1 1;
+     0 0 1 1 1 0 1 1 0 1 0 1;
+     0 1 1 1 0 1 1 0 1 0 0 1;
+     1 1 1 0 1 1 0 1 0 0 0 1;
+     1 1 0 1 1 0 1 0 0 0 1 1;
+     1 0 1 1 0 1 0 0 0 1 1 1;
+     0 1 1 0 1 0 0 0 1 1 1 1;
+     1 1 0 1 0 0 0 1 1 1 0 1;
+     1 0 1 0 0 0 1 1 1 0 1 1;
+     0 1 0 0 0 1 1 1 0 1 1 1;
+     1 1 1 1 1 1 1 1 1 1 1 0;];
+
+  H=[I; P]; %partiy check matrix transpose.
+
+  dec_error=[];
+  C=zeros(size(R));
+
+  for rspn=1:rows(R)
+    RR=R(rspn,:);
+    S=mod(RR*H,2);
+    wt=sum(S);
+    done=0;
+    if (wt <= 3)
+      E=[S, zeros(1,12)];
+      done=1;
+    else
+      SP = mod(repmat(S,[12, 1])+P,2);
+      idx = find( sum(SP,2) <= 2 );    
+      if ( idx )
+        idx=idx(1); %pick first of matches.
+        Ui=zeros(1,12); Ui(idx)=1;
+        E=[SP(idx,:),Ui];
+        done=1;
+      end
+    end
+
+    if ( ~done )
+      X=mod(S*P,2);
+      wt=sum(X);
+      if (wt==2 || wt==3)
+        E=[zeros(1,12), X];
+        done=1;
+      else
+        SP = mod(repmat(X,[12, 1])+P,2);
+        idx = find( sum(SP,2) == 2 );
+        if ( idx )
+          idx=idx(1);
+          Ui=zeros(1,12); Ui(idx)=1;
+          E=[Ui,SP(idx,:)];
+          done=1;
+        end
+      end
+    end
+
+    dec_error=[dec_error; 1-done];
+    C(rspn,:)=mod(E+RR,2);
+  end
+
+  return;
+end
+                                %!
+                                %!assert(egolaydec([1 1 1 zeros(1,21)]),zeros(1,24))
+                                %!assert(egolaydec([1 0 1 zeros(1,20) 1]),zeros(1,24))
+                                %!
+
+